ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC

Closure property of random sum and its maximum of random variables from class D based on precise large deviation principles

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2019.05.006
  • Received Date: 31 May 2018
  • Rev Recd Date: 03 June 2019
  • Publish Date: 31 May 2019
  • Let X={X1,X2,…} be a sequence of independent but not necessarily identically distributed random variables,and let η be an integer-valued counting random variable independent of X.Random sum Sη=∑ηk=1 Xk and its maximum S(η)=max{S0,…,Sη} were studied. Assuming that each Xk belongs to the class of D, by using the result of the precise large deviation principles on class D, it was proven that the distributions of Sη and S(η) belong to the same class under some conditions.The obtained results expand the related ones of previous studies.
    Let X={X1,X2,…} be a sequence of independent but not necessarily identically distributed random variables,and let η be an integer-valued counting random variable independent of X.Random sum Sη=∑ηk=1 Xk and its maximum S(η)=max{S0,…,Sη} were studied. Assuming that each Xk belongs to the class of D, by using the result of the precise large deviation principles on class D, it was proven that the distributions of Sη and S(η) belong to the same class under some conditions.The obtained results expand the related ones of previous studies.
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